14.25 A mass attached to a spring is free to oscillate, with angular velocity $\mathit{\omega }$ , in a horizontal plane without friction or damping. It is pulled to a distance ${\mathit{x}}_0$ and pushed towards the centre with a velocity ${\mathit{v}}_0\mathit{}$ at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters $\mathit{\omega },\mathit{}{\mathit{x}}_0\mathit{}$ and ${\mathit{v}}_0$ .

[Hint : Start with the equation x = a cos ( $\mathit{\omega }$ t + $\mathit{\theta }$ ) and note that the initial velocity is negative.]

If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. New amplitude of oscillation will be:

The fundamental frequency of an organ pipe open at one end is 300 Hz. The frequency of 3rd overtone of n Find n.×this organ pipe is 100 Hz

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is T_b / T_a = √x, where value of x is ................... (Round off to the Nearest Integer)

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
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